What is x^3(x-1)>= 2x^2(6-x) ?

The solution to x^3(x-1)>= 2x^2(6-x) is x = 3

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x^3(x-1)>= 2x^2(6-x)

x^{3} (x - 1) \geq 2 x^{2} (6 - x)

x \leq - 4 or x = 0 or x \geq 3

Interval Notation

(- \infty, - 4] \cup x = 0 \cup [3, \infty)

Solution steps

x^{3} (x - 1) \geq 2 x^{2} (6 - x)

Rewrite in standard form

x^{4} + x^{3} - 12 x^{2} \geq 0

Factor

x^{4} + x^{3} - 12 x^{2} : x^{2} (x - 3) (x + 4)

x^{2} (x - 3) (x + 4) \geq 0

Identify the intervals

x \leq - 4 or x = 0 or x \geq 3

16 x - x^{2}

\frac{- 4}{3}

9 u^{2} - 49 v^{2}

\frac{72}{- 9}

\frac{3}{2} x + 4 \leq 10

What is x^3(x-1)>= 2x^2(6-x) ?
The solution to x^3(x-1)>= 2x^2(6-x) is x<=-4\lor x=0\lor x>= 3